I have found what appears to be a bug in version 5.6.1 of:
~\DesktopModules\Admin\Authentication\Login.ascx.vb

In the BindLogin() method, the logic retrieves all the enabled authentication providers and looks for an enabled login control.  However, it never finds one because the following if statement *never* evaluates to True!  Even for the default DNN Authenticator!

'Check if AuthSystem is Enabled
If authLoginControl.Enabled Then
    'Add Login Control to List
    loginControls.Add(authLoginControl)
End If

The reason the login process succeeds is due to this  logic (further down):

'No enabled controls - inject default dnn control
                    If defaultLoginControl Is Nothing Then
                        'No controls enabled for portal, and default DNN control is not enabled by host, so load system default (DNN)
                        Dim authSystem As AuthenticationInfo = AuthenticationController.GetAuthenticationServiceByType("DNN")
                        Dim authLoginControl As AuthenticationLoginBase = CType(LoaodControl("~/" & authSystem.LoginControlSrc), AuthenticationLoginBase)
                        BindLoginControl(authLoginControl, authSystem)
                        DisplayLoginControl(authLoginControl, False, False)
                    Else

How are login controls "enabled"?